
In the example of the spring, the static operating curve shown in
Figure 7.48 can be divi ded into three distinct regions, that is,
points {F, x(F )} where
1. F
min
< F < F
1
2. F
1
F F
2
(linear region)
3. F
2
< F < F
max
The relation x ¼x(F ) between force and displacement in each
region is based on empirical observation as opposed to an analyt-
ical model or equation based o n scientific principles or natural
laws. In contrast, the liquid tank with incompressible fluid shown
in Figure 7.49 is modeled by the linear first-order differential
equation based on conservation of volume,
A
dH
dt
þ F
0
¼ F
1
(7:88)
along with the operating characteristic of the tank, that is, ...